The SO(3) × SO(3) × U(1) hubbard model on a square lattice in terms of c and αν fermions and deconfined η-spinons and spinons

Abstract

In this paper, a general description for the Hubbard model with nearest-neighbor transfer integral t and on-site repulsion U on a square lattice with N2 a ≫ 1 sites is introduced. It refers to three types of elementary objects whose occupancy configurations generate the state representations of the model extended global SO(3) × SO(3) × U(1) symmetry recently found in Ref. [11] (Carmelo and Östlund, 2010). Such objects emerge from a suitable electron–rotated-electron unitary transformation. It is such that rotated-electron single and double occupancy are good quantum numbers for U ̸= 0. The advantage of the description is that it accounts for the new found hidden U(1) symmetry in SO(3) × SO(3)×U(1) = [SU(2)×SU(2)×U(1)]/Z2 2 beyond the well-known SO(4) = [SU(2) × SU(2)]/Z2 model (partial) global symmetry. Specifically, the hidden U(1) symmetry state representations store full information on the positions of the spins of the rotated-electron singly occupied sites relative to the remaining sites. Profiting from that complementary information, for the whole U/4t > 0 interaction range independent spin state representations are naturally generated in terms of spin-1/2 spinon occupancy configurations in a spin effective lattice. For all states, such an effective lattice has as many sites as spinons. This allows the extension to intermediate U/4t values of the usual large-U/4t descriptions of the spin degrees of freedom of the electrons that singly occupy sites, now in terms of the spins of the singly-occupied sites rotated electrons. The operator description introduced in this paper brings about a more suitable scenario for handling the effects of hole doping. Within this, such effects are accounted for in terms of the residual interactions of the elementary objects whose occupancy configurations generate the state representations of the charge hidden U(1) symmetry and spin SU(2) symmetry, respectively. This problem is investigated elsewhere. The most interesting physical information revealed by the description refers to the model on the subspace generated by the application of one- and two-electron operators onto zero-magnetization ground states. (This is the square-lattice quantum liquid further studied in Ref. [5] (Carmelo, 2010).) However, to access such an information, one must start from the general description introduced in this paper, which refers to the model in the full Hilbert space.